Zintl rule

A traditional example of a Zintl phase is represented by NaTl which may be considered as a prototype of the Zintl rules. The structure of this compound (face centred cubic, cF16, a = 747.3 pm) can be described (see also 7.4.2.2.) as resulting from two interpenetrating diamond type lattices corresponding to the arrangements of the Na and T1 atoms respectively (Zintl and Dullenkopf 1932). Each T1 atom therefore is coordinated to other four T1 at a distance a)3/4 = 747.3)3/4 = 323.6pm which is shorter than that observed in elemental thallium (d = 341-346 pm in aTl, hP2-Mg type, CN = 6 + 6) and d = 336pm in /3 Tl, (cI2-W type, CN = 8). 

Regardless of their possible metallic properties, metal-rich Zintl system or phases are defined here as cation-rich compounds exhibiting anionic moieties of metal or metalloid elements whose structures can be generally understood by applying the classical or modern electron counting rules for molecules. 

As we can see from the last entry in this table, we have deduced only a rule. In InBi there are Bi-Bi contacts and it has metallic properties. Further examples that do not fulfill the rule are LiPb (Pb atoms surrounded only by Li) and K8Ge46. In the latter, all Ge atoms have four covalent bonds they form a wide-meshed framework that encloses the K+ ions (Fig. 16.26, p. 188) the electrons donated by the potassium atoms are not taken over by the germanium, and instead they form a band. In a way, this is a kind of a solid solution, with germanium as solvent for K+ and solvated electrons. K8Ge46 has metallic properties. In the sense of the 8-A rule the metallic electrons can be captured in K8Ga8Ge38, which has the same structure, all the electrons of the potassium are required for the framework, and it is a semiconductor. In spite of the exceptions, the concept has turned out to be very fruitful, especially in the context of understanding the Zintl phases. 

Polar intermetallics are loosely referred to as electron-poorer relatives of Zintl phases in which the active metals do not contribute all of their valence electrons, rather they bond with the more electronegative components to some degree. The structures cannot be simply accounted for by octet rules because of substantial delocalized bonding among the atoms. 

As mentioned in the Introduction, no structural information on these species was available for more than 40 years after the discovery of the first Zintl metal cluster anions, since no pure crystalline phases could be isolated and characterized structurally. Nevertheless, early efforts to rationalize the observed formulas and chemical bonding of these intermetallics and related molecules utilized the Zintl-Klemm concept [75, 76] and the Mooser-Pearson [77] extended (8 — N) rule. In this rule N refers to the number of valence electrons of the more electronegative metal (and thus anionic metal) in the intermetallic phases. 

The same rules may be applied to the Zintl anion Bobserved in compounds such as CaB6 and corresponding to a framework of corner-sharing boron octahedra as described in the following 4.4.4.7. 

Abstract This chapter reviews the methods that are useful for understanding the structure and bonding in Zintl ions and related bare post-transition element clusters in approximate historical order. After briefly discussing the Zintl-Klemm model the Wade-Mingos rules and related ideas are discussed. The chapter concludes with a discussion of the jellium model and special methods pertaining to bare metal clusters with interstitial atoms. 

Keywords Jellium model Metal clusters Wade-Mingos rules Zintl ions Contents... 

Early efforts to rationalize the observed formulas and chemical bonding of Zintl ions and related species used initially the Zintl-Klemm concept [10, 11] and subsequently the Mooser-Pearson [12] extended (8 — AO rule. In this rule, refers... 

For a general formulation of the Zintl-Klemm concept, consider an intermetallic AmX phase, where A is the more electropositive element, t3 pically an alkali or an alkaline earth metal. Both A and X, viewed as individual atoms, are assumed to follow the octet rule leading to transfer of electrons from A to X, i.e., A AF, X —> X , so that mp = nq. The anionic unit X arising from this electron transfer is considered to be a pseudoatom, which exhibits a structural chemistry closely related to that of the isoelectronic elements [11]. Since bonding also is possible in the cationic units, the numbers of electrons involved in A-A and X-X bonds of various types (caa and exx> respectively) as well as the number of electrons e not involved in localized bonds can be generated from the numbers of valence electrons on A and X, namely and ex, respectively, by the following equations of balance ... 

The Relationship of Zintl Ions to Polyhedral Boranes The Wade-Mingos Rules and the Aromaticity of Clusters... 

The next development in the understanding of structure and bonding in the Zintl ions recognized their relationship to the polyhedral boranes and the isoelectronic carboranes. Then the Wade-Mingos rules [13-16], which were developed to understand the structure and bonding in polyhedral boranes, could be extended to isovalent Zintl ions and related post-transition element clusters. 

Electron count according to the (8-N) rule and the Zintl-Klemm concept... 

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